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<div class="header">
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<a href="classEigen_1_1FullPivHouseholderQR-members.html">List of all members</a> &#124;
<a href="#pub-methods">Public Member Functions</a>  </div>
  <div class="headertitle">
<div class="title">Eigen::FullPivHouseholderQR&lt; MatrixType_ &gt; Class Template Reference<div class="ingroups"><a class="el" href="group__DenseLinearSolvers__chapter.html">Dense linear problems and decompositions</a> &raquo; <a class="el" href="group__DenseLinearSolvers__Reference.html">Reference</a> &raquo; <a class="el" href="group__QR__Module.html">QR module</a></div></div>  </div>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><h3>template&lt;typename MatrixType_&gt;<br />
class Eigen::FullPivHouseholderQR&lt; MatrixType_ &gt;</h3>

<p>Householder rank-revealing QR decomposition of a matrix with full pivoting. </p>
<dl class="tparams"><dt>Template Parameters</dt><dd>
  <table class="tparams">
    <tr><td class="paramname">MatrixType_</td><td>the type of the matrix of which we are computing the QR decomposition</td></tr>
  </table>
  </dd>
</dl>
<p>This class performs a rank-revealing QR decomposition of a matrix <b>A</b> into matrices <b>P</b>, <b>P'</b>, <b>Q</b> and <b>R</b> such that </p><p class="formulaDsp">
\[ \mathbf{P} \, \mathbf{A} \, \mathbf{P}&#39; = \mathbf{Q} \, \mathbf{R} \]
</p>
<p> by using Householder transformations. Here, <b>P</b> and <b>P'</b> are permutation matrices, <b>Q</b> a unitary matrix and <b>R</b> an upper triangular matrix.</p>
<p>This decomposition performs a very prudent full pivoting in order to be rank-revealing and achieve optimal numerical stability. The trade-off is that it is slower than <a class="el" href="classEigen_1_1HouseholderQR.html" title="Householder QR decomposition of a matrix.">HouseholderQR</a> and <a class="el" href="classEigen_1_1ColPivHouseholderQR.html" title="Householder rank-revealing QR decomposition of a matrix with column-pivoting.">ColPivHouseholderQR</a>.</p>
<p>This class supports the <a class="el" href="group__InplaceDecomposition.html">inplace decomposition </a> mechanism.</p>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="classEigen_1_1MatrixBase.html#a863bc0e06b641a089508eabec6835ab2">MatrixBase::fullPivHouseholderQr()</a> </dd></dl>
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  <img id="dynsection-0-trigger" src="closed.png" alt="+"/> Inheritance diagram for Eigen::FullPivHouseholderQR&lt; MatrixType_ &gt;:</div>
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<div class="center"><img src="classEigen_1_1FullPivHouseholderQR__inherit__graph.png" border="0" usemap="#aEigen_1_1FullPivHouseholderQR_3_01MatrixType___01_4_inherit__map" alt="Inheritance graph"/></div>
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<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr class="memitem:a1029e1ccc70bb8669043c5775e7f3b75"><td class="memItemLeft" align="right" valign="top">MatrixType::RealScalar&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivHouseholderQR.html#a1029e1ccc70bb8669043c5775e7f3b75">absDeterminant</a> () const</td></tr>
<tr class="separator:a1029e1ccc70bb8669043c5775e7f3b75"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aa287da5c27b6ad8e54466be392e59353"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1PermutationMatrix.html">PermutationType</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivHouseholderQR.html#aa287da5c27b6ad8e54466be392e59353">colsPermutation</a> () const</td></tr>
<tr class="separator:aa287da5c27b6ad8e54466be392e59353"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:af06caae23f1f17878ae8ff0c0cd7b899"><td class="memTemplParams" colspan="2">template&lt;typename InputType &gt; </td></tr>
<tr class="memitem:af06caae23f1f17878ae8ff0c0cd7b899"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1FullPivHouseholderQR.html">FullPivHouseholderQR</a>&lt; MatrixType &gt; &amp;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivHouseholderQR.html#af06caae23f1f17878ae8ff0c0cd7b899">compute</a> (const <a class="el" href="structEigen_1_1EigenBase.html">EigenBase</a>&lt; InputType &gt; &amp;matrix)</td></tr>
<tr class="separator:af06caae23f1f17878ae8ff0c0cd7b899"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a397b69cf6016ccc634bb1ec3565604ef"><td class="memItemLeft" align="right" valign="top"><a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivHouseholderQR.html#a397b69cf6016ccc634bb1ec3565604ef">dimensionOfKernel</a> () const</td></tr>
<tr class="separator:a397b69cf6016ccc634bb1ec3565604ef"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a8daa52818d7861e1fc9b6aeee265701d"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivHouseholderQR.html#a8daa52818d7861e1fc9b6aeee265701d">FullPivHouseholderQR</a> ()</td></tr>
<tr class="memdesc:a8daa52818d7861e1fc9b6aeee265701d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Default Constructor.  <a href="classEigen_1_1FullPivHouseholderQR.html#a8daa52818d7861e1fc9b6aeee265701d">More...</a><br /></td></tr>
<tr class="separator:a8daa52818d7861e1fc9b6aeee265701d"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a105fbc288850fb59e67d19a42ebfad88"><td class="memTemplParams" colspan="2">template&lt;typename InputType &gt; </td></tr>
<tr class="memitem:a105fbc288850fb59e67d19a42ebfad88"><td class="memTemplItemLeft" align="right" valign="top">&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivHouseholderQR.html#a105fbc288850fb59e67d19a42ebfad88">FullPivHouseholderQR</a> (const <a class="el" href="structEigen_1_1EigenBase.html">EigenBase</a>&lt; InputType &gt; &amp;matrix)</td></tr>
<tr class="memdesc:a105fbc288850fb59e67d19a42ebfad88"><td class="mdescLeft">&#160;</td><td class="mdescRight">Constructs a QR factorization from a given matrix.  <a href="classEigen_1_1FullPivHouseholderQR.html#a105fbc288850fb59e67d19a42ebfad88">More...</a><br /></td></tr>
<tr class="separator:a105fbc288850fb59e67d19a42ebfad88"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a66226b1bcaf4aedcc63fd2ef00b40e8e"><td class="memTemplParams" colspan="2">template&lt;typename InputType &gt; </td></tr>
<tr class="memitem:a66226b1bcaf4aedcc63fd2ef00b40e8e"><td class="memTemplItemLeft" align="right" valign="top">&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivHouseholderQR.html#a66226b1bcaf4aedcc63fd2ef00b40e8e">FullPivHouseholderQR</a> (<a class="el" href="structEigen_1_1EigenBase.html">EigenBase</a>&lt; InputType &gt; &amp;matrix)</td></tr>
<tr class="memdesc:a66226b1bcaf4aedcc63fd2ef00b40e8e"><td class="mdescLeft">&#160;</td><td class="mdescRight">Constructs a QR factorization from a given matrix.  <a href="classEigen_1_1FullPivHouseholderQR.html#a66226b1bcaf4aedcc63fd2ef00b40e8e">More...</a><br /></td></tr>
<tr class="separator:a66226b1bcaf4aedcc63fd2ef00b40e8e"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a68844bff2b25a02d3228bed10c7365d5"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivHouseholderQR.html#a68844bff2b25a02d3228bed10c7365d5">FullPivHouseholderQR</a> (<a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> rows, <a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> cols)</td></tr>
<tr class="memdesc:a68844bff2b25a02d3228bed10c7365d5"><td class="mdescLeft">&#160;</td><td class="mdescRight">Default Constructor with memory preallocation.  <a href="classEigen_1_1FullPivHouseholderQR.html#a68844bff2b25a02d3228bed10c7365d5">More...</a><br /></td></tr>
<tr class="separator:a68844bff2b25a02d3228bed10c7365d5"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a9ef597fe70c9f5543195412e77a019c5"><td class="memItemLeft" align="right" valign="top">const HCoeffsType &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivHouseholderQR.html#a9ef597fe70c9f5543195412e77a019c5">hCoeffs</a> () const</td></tr>
<tr class="separator:a9ef597fe70c9f5543195412e77a019c5"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aee67714eb16a2f4f8ed9cb630a10cf2b"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1Inverse.html">Inverse</a>&lt; <a class="el" href="classEigen_1_1FullPivHouseholderQR.html">FullPivHouseholderQR</a> &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivHouseholderQR.html#aee67714eb16a2f4f8ed9cb630a10cf2b">inverse</a> () const</td></tr>
<tr class="separator:aee67714eb16a2f4f8ed9cb630a10cf2b"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aaabe67945b11eebe93a8c86ab9ea535f"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivHouseholderQR.html#aaabe67945b11eebe93a8c86ab9ea535f">isInjective</a> () const</td></tr>
<tr class="separator:aaabe67945b11eebe93a8c86ab9ea535f"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a56f77373a9075a236f3a12c597aa6596"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivHouseholderQR.html#a56f77373a9075a236f3a12c597aa6596">isInvertible</a> () const</td></tr>
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<tr class="memitem:ae168dea30894ed413a513c438aa4399b"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivHouseholderQR.html#ae168dea30894ed413a513c438aa4399b">isSurjective</a> () const</td></tr>
<tr class="separator:ae168dea30894ed413a513c438aa4399b"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aafde38918912c9b562f44b0fc3b22589"><td class="memItemLeft" align="right" valign="top">MatrixType::RealScalar&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivHouseholderQR.html#aafde38918912c9b562f44b0fc3b22589">logAbsDeterminant</a> () const</td></tr>
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<tr class="memitem:ad26dd2d3c002939771d2375e4e051c28"><td class="memItemLeft" align="right" valign="top">MatrixQReturnType&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivHouseholderQR.html#ad26dd2d3c002939771d2375e4e051c28">matrixQ</a> (void) const</td></tr>
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<tr class="memitem:ab082b221dc32cf25a951f0f822b78337"><td class="memItemLeft" align="right" valign="top">const MatrixType &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivHouseholderQR.html#ab082b221dc32cf25a951f0f822b78337">matrixQR</a> () const</td></tr>
<tr class="separator:ab082b221dc32cf25a951f0f822b78337"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ac00d0f43ded3debd5c1769fd0a09c884"><td class="memItemLeft" align="right" valign="top">RealScalar&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivHouseholderQR.html#ac00d0f43ded3debd5c1769fd0a09c884">maxPivot</a> () const</td></tr>
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<tr class="memitem:a15bac4e5678baeb4f26c9b2fb588415d"><td class="memItemLeft" align="right" valign="top"><a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivHouseholderQR.html#a15bac4e5678baeb4f26c9b2fb588415d">nonzeroPivots</a> () const</td></tr>
<tr class="separator:a15bac4e5678baeb4f26c9b2fb588415d"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a8f700c9adb9928a7cf801880946d66ff"><td class="memItemLeft" align="right" valign="top"><a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivHouseholderQR.html#a8f700c9adb9928a7cf801880946d66ff">rank</a> () const</td></tr>
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<tr class="memitem:ad136fe1c4b1ebd37aeb0e28c31386ffc"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1Matrix.html">IntDiagSizeVectorType</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivHouseholderQR.html#ad136fe1c4b1ebd37aeb0e28c31386ffc">rowsTranspositions</a> () const</td></tr>
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<tr class="memitem:ac86022d45b8b0ed0c004852affcb9ec6"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1FullPivHouseholderQR.html">FullPivHouseholderQR</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivHouseholderQR.html#ac86022d45b8b0ed0c004852affcb9ec6">setThreshold</a> (const RealScalar &amp;<a class="el" href="classEigen_1_1FullPivHouseholderQR.html#adbb357dc50ae6fa6f51eb785e9d85403">threshold</a>)</td></tr>
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<tr class="memitem:ac20e4ce2bb07cd2f77fca60ad7a788f3"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1FullPivHouseholderQR.html">FullPivHouseholderQR</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivHouseholderQR.html#ac20e4ce2bb07cd2f77fca60ad7a788f3">setThreshold</a> (Default_t)</td></tr>
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<tr class="memitem:aad55fd4eaf0905b7dc092e7f1615b489"><td class="memTemplParams" colspan="2">template&lt;typename Rhs &gt; </td></tr>
<tr class="memitem:aad55fd4eaf0905b7dc092e7f1615b489"><td class="memTemplItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1Solve.html">Solve</a>&lt; <a class="el" href="classEigen_1_1FullPivHouseholderQR.html">FullPivHouseholderQR</a>, Rhs &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivHouseholderQR.html#aad55fd4eaf0905b7dc092e7f1615b489">solve</a> (const <a class="el" href="classEigen_1_1MatrixBase.html">MatrixBase</a>&lt; Rhs &gt; &amp;b) const</td></tr>
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<tr class="memitem:adbb357dc50ae6fa6f51eb785e9d85403"><td class="memItemLeft" align="right" valign="top">RealScalar&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivHouseholderQR.html#adbb357dc50ae6fa6f51eb785e9d85403">threshold</a> () const</td></tr>
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<tr class="inherit_header pub_methods_classEigen_1_1SolverBase"><td colspan="2" onclick="javascript:toggleInherit('pub_methods_classEigen_1_1SolverBase')"><img src="closed.png" alt="-"/>&#160;Public Member Functions inherited from <a class="el" href="classEigen_1_1SolverBase.html">Eigen::SolverBase&lt; FullPivHouseholderQR&lt; MatrixType_ &gt; &gt;</a></td></tr>
<tr class="memitem:ae1025416bdb5a768f7213c67feb4dc33 inherit pub_methods_classEigen_1_1SolverBase"><td class="memItemLeft" align="right" valign="top">const AdjointReturnType&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SolverBase.html#ae1025416bdb5a768f7213c67feb4dc33">adjoint</a> () const</td></tr>
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<tr class="memitem:a1fbabe7f12bcbfba3b9a448b1f5e46fa inherit pub_methods_classEigen_1_1SolverBase"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1FullPivHouseholderQR.html">FullPivHouseholderQR</a>&lt; MatrixType_ &gt; &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SolverBase.html#a1fbabe7f12bcbfba3b9a448b1f5e46fa">derived</a> ()</td></tr>
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<tr class="memitem:afd4f3f1c57b7594b96a7e30f2974ea2e inherit pub_methods_classEigen_1_1SolverBase"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1FullPivHouseholderQR.html">FullPivHouseholderQR</a>&lt; MatrixType_ &gt; &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SolverBase.html#afd4f3f1c57b7594b96a7e30f2974ea2e">derived</a> () const</td></tr>
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<tr class="memitem:a7fd647d110487799205df6f99547879d inherit pub_methods_classEigen_1_1SolverBase"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1Solve.html">Solve</a>&lt; <a class="el" href="classEigen_1_1FullPivHouseholderQR.html">FullPivHouseholderQR</a>&lt; MatrixType_ &gt;, Rhs &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SolverBase.html#a7fd647d110487799205df6f99547879d">solve</a> (const <a class="el" href="classEigen_1_1MatrixBase.html">MatrixBase</a>&lt; Rhs &gt; &amp;b) const</td></tr>
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<tr class="memitem:a4d5e5baddfba3790ab1a5f247dcc4dc1 inherit pub_methods_classEigen_1_1SolverBase"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SolverBase.html#a4d5e5baddfba3790ab1a5f247dcc4dc1">SolverBase</a> ()</td></tr>
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<tr class="memitem:a70cf5cd1b31dbb4f4d61c436c83df6d3 inherit pub_methods_classEigen_1_1SolverBase"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1Transpose.html">ConstTransposeReturnType</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SolverBase.html#a70cf5cd1b31dbb4f4d61c436c83df6d3">transpose</a> () const</td></tr>
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<tr class="inherit_header pub_methods_structEigen_1_1EigenBase"><td colspan="2" onclick="javascript:toggleInherit('pub_methods_structEigen_1_1EigenBase')"><img src="closed.png" alt="-"/>&#160;Public Member Functions inherited from <a class="el" href="structEigen_1_1EigenBase.html">Eigen::EigenBase&lt; Derived &gt;</a></td></tr>
<tr class="memitem:a2d768a9877f5f69f49432d447b552bfe inherit pub_methods_structEigen_1_1EigenBase"><td class="memItemLeft" align="right" valign="top">EIGEN_CONSTEXPR <a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1EigenBase.html#a2d768a9877f5f69f49432d447b552bfe">cols</a> () const EIGEN_NOEXCEPT</td></tr>
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<tr class="memitem:a1fbabe7f12bcbfba3b9a448b1f5e46fa inherit pub_methods_structEigen_1_1EigenBase"><td class="memItemLeft" align="right" valign="top">Derived &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1EigenBase.html#a1fbabe7f12bcbfba3b9a448b1f5e46fa">derived</a> ()</td></tr>
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<tr class="memitem:afd4f3f1c57b7594b96a7e30f2974ea2e inherit pub_methods_structEigen_1_1EigenBase"><td class="memItemLeft" align="right" valign="top">const Derived &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1EigenBase.html#afd4f3f1c57b7594b96a7e30f2974ea2e">derived</a> () const</td></tr>
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<tr class="memitem:ac22eb0695d00edd7d4a3b2d0a98b81c2 inherit pub_methods_structEigen_1_1EigenBase"><td class="memItemLeft" align="right" valign="top">EIGEN_CONSTEXPR <a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1EigenBase.html#ac22eb0695d00edd7d4a3b2d0a98b81c2">rows</a> () const EIGEN_NOEXCEPT</td></tr>
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<tr class="memitem:ae106171b6fefd3f7af108a8283de36c9 inherit pub_methods_structEigen_1_1EigenBase"><td class="memItemLeft" align="right" valign="top">EIGEN_CONSTEXPR <a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1EigenBase.html#ae106171b6fefd3f7af108a8283de36c9">size</a> () const EIGEN_NOEXCEPT</td></tr>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="inherited"></a>
Additional Inherited Members</h2></td></tr>
<tr class="inherit_header pub_types_structEigen_1_1EigenBase"><td colspan="2" onclick="javascript:toggleInherit('pub_types_structEigen_1_1EigenBase')"><img src="closed.png" alt="-"/>&#160;Public Types inherited from <a class="el" href="structEigen_1_1EigenBase.html">Eigen::EigenBase&lt; Derived &gt;</a></td></tr>
<tr class="memitem:a554f30542cc2316add4b1ea0a492ff02 inherit pub_types_structEigen_1_1EigenBase"><td class="memItemLeft" align="right" valign="top">typedef <a class="el" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Eigen::Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a></td></tr>
<tr class="memdesc:a554f30542cc2316add4b1ea0a492ff02 inherit pub_types_structEigen_1_1EigenBase"><td class="mdescLeft">&#160;</td><td class="mdescRight">The interface type of indices.  <a href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">More...</a><br /></td></tr>
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<h2 class="groupheader">Constructor &amp; Destructor Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a8daa52818d7861e1fc9b6aeee265701d">&#9670;&nbsp;</a></span>FullPivHouseholderQR() <span class="overload">[1/4]</span></h2>

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<p>Default Constructor. </p>
<p>The default constructor is useful in cases in which the user intends to perform decompositions via FullPivHouseholderQR::compute(const MatrixType&amp;). </p>

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<h2 class="memtitle"><span class="permalink"><a href="#a68844bff2b25a02d3228bed10c7365d5">&#9670;&nbsp;</a></span>FullPivHouseholderQR() <span class="overload">[2/4]</span></h2>

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          <td>(</td>
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<p>Default Constructor with memory preallocation. </p>
<p>Like the default constructor but with preallocation of the internal data according to the specified problem <em>size</em>. </p><dl class="section see"><dt>See also</dt><dd><a class="el" href="classEigen_1_1FullPivHouseholderQR.html#a8daa52818d7861e1fc9b6aeee265701d" title="Default Constructor.">FullPivHouseholderQR()</a> </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a105fbc288850fb59e67d19a42ebfad88">&#9670;&nbsp;</a></span>FullPivHouseholderQR() <span class="overload">[3/4]</span></h2>

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<p>Constructs a QR factorization from a given matrix. </p>
<p>This constructor computes the QR factorization of the matrix <em>matrix</em> by calling the method compute(). It is a short cut for:</p>
<div class="fragment"><div class="line">FullPivHouseholderQR&lt;MatrixType&gt; qr(matrix.rows(), matrix.cols());</div>
<div class="line">qr.compute(matrix);</div>
</div><!-- fragment --><dl class="section see"><dt>See also</dt><dd>compute() </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a66226b1bcaf4aedcc63fd2ef00b40e8e">&#9670;&nbsp;</a></span>FullPivHouseholderQR() <span class="overload">[4/4]</span></h2>

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<p>Constructs a QR factorization from a given matrix. </p>
<p>This overloaded constructor is provided for <a class="el" href="group__InplaceDecomposition.html">inplace decomposition </a> when <code>MatrixType</code> is a <a class="el" href="classEigen_1_1Ref.html" title="A matrix or vector expression mapping an existing expression.">Eigen::Ref</a>.</p>
<dl class="section see"><dt>See also</dt><dd>FullPivHouseholderQR(const EigenBase&amp;) </dd></dl>

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<h2 class="groupheader">Member Function Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a1029e1ccc70bb8669043c5775e7f3b75">&#9670;&nbsp;</a></span>absDeterminant()</h2>

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<dl class="section return"><dt>Returns</dt><dd>the absolute value of the determinant of the matrix of which *this is the QR decomposition. It has only linear complexity (that is, O(n) where n is the dimension of the square matrix) as the QR decomposition has already been computed.</dd></dl>
<dl class="section note"><dt>Note</dt><dd>This is only for square matrices.</dd></dl>
<dl class="section warning"><dt>Warning</dt><dd>a determinant can be very big or small, so for matrices of large enough dimension, there is a risk of overflow/underflow. One way to work around that is to use <a class="el" href="classEigen_1_1FullPivHouseholderQR.html#aafde38918912c9b562f44b0fc3b22589">logAbsDeterminant()</a> instead.</dd></dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="classEigen_1_1FullPivHouseholderQR.html#aafde38918912c9b562f44b0fc3b22589">logAbsDeterminant()</a>, <a class="el" href="classEigen_1_1MatrixBase.html#a7ad8f77004bb956b603bb43fd2e3c061">MatrixBase::determinant()</a> </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#aa287da5c27b6ad8e54466be392e59353">&#9670;&nbsp;</a></span>colsPermutation()</h2>

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<dl class="section return"><dt>Returns</dt><dd>a const reference to the column permutation matrix </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#af06caae23f1f17878ae8ff0c0cd7b899">&#9670;&nbsp;</a></span>compute()</h2>

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<p>Performs the QR factorization of the given matrix <em>matrix</em>. The result of the factorization is stored into <code>*this</code>, and a reference to <code>*this</code> is returned.</p>
<dl class="section see"><dt>See also</dt><dd>class <a class="el" href="classEigen_1_1FullPivHouseholderQR.html" title="Householder rank-revealing QR decomposition of a matrix with full pivoting.">FullPivHouseholderQR</a>, FullPivHouseholderQR(const MatrixType&amp;) </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a397b69cf6016ccc634bb1ec3565604ef">&#9670;&nbsp;</a></span>dimensionOfKernel()</h2>

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<dl class="section return"><dt>Returns</dt><dd>the dimension of the kernel of the matrix of which *this is the QR decomposition.</dd></dl>
<dl class="section note"><dt>Note</dt><dd>This method has to determine which pivots should be considered nonzero. For that, it uses the threshold value that you can control by calling <a class="el" href="classEigen_1_1FullPivHouseholderQR.html#ac86022d45b8b0ed0c004852affcb9ec6">setThreshold(const RealScalar&amp;)</a>. </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a9ef597fe70c9f5543195412e77a019c5">&#9670;&nbsp;</a></span>hCoeffs()</h2>

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<dl class="section return"><dt>Returns</dt><dd>a const reference to the vector of Householder coefficients used to represent the factor <code>Q</code>.</dd></dl>
<p>For advanced uses only. </p>

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<h2 class="memtitle"><span class="permalink"><a href="#aee67714eb16a2f4f8ed9cb630a10cf2b">&#9670;&nbsp;</a></span>inverse()</h2>

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<dl class="section return"><dt>Returns</dt><dd>the inverse of the matrix of which *this is the QR decomposition.</dd></dl>
<dl class="section note"><dt>Note</dt><dd>If this matrix is not invertible, the returned matrix has undefined coefficients. Use <a class="el" href="classEigen_1_1FullPivHouseholderQR.html#a56f77373a9075a236f3a12c597aa6596">isInvertible()</a> to first determine whether this matrix is invertible. </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#aaabe67945b11eebe93a8c86ab9ea535f">&#9670;&nbsp;</a></span>isInjective()</h2>

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<dl class="section return"><dt>Returns</dt><dd>true if the matrix of which *this is the QR decomposition represents an injective linear map, i.e. has trivial kernel; false otherwise.</dd></dl>
<dl class="section note"><dt>Note</dt><dd>This method has to determine which pivots should be considered nonzero. For that, it uses the threshold value that you can control by calling <a class="el" href="classEigen_1_1FullPivHouseholderQR.html#ac86022d45b8b0ed0c004852affcb9ec6">setThreshold(const RealScalar&amp;)</a>. </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a56f77373a9075a236f3a12c597aa6596">&#9670;&nbsp;</a></span>isInvertible()</h2>

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<dl class="section return"><dt>Returns</dt><dd>true if the matrix of which *this is the QR decomposition is invertible.</dd></dl>
<dl class="section note"><dt>Note</dt><dd>This method has to determine which pivots should be considered nonzero. For that, it uses the threshold value that you can control by calling <a class="el" href="classEigen_1_1FullPivHouseholderQR.html#ac86022d45b8b0ed0c004852affcb9ec6">setThreshold(const RealScalar&amp;)</a>. </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#ae168dea30894ed413a513c438aa4399b">&#9670;&nbsp;</a></span>isSurjective()</h2>

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<dl class="section return"><dt>Returns</dt><dd>true if the matrix of which *this is the QR decomposition represents a surjective linear map; false otherwise.</dd></dl>
<dl class="section note"><dt>Note</dt><dd>This method has to determine which pivots should be considered nonzero. For that, it uses the threshold value that you can control by calling <a class="el" href="classEigen_1_1FullPivHouseholderQR.html#ac86022d45b8b0ed0c004852affcb9ec6">setThreshold(const RealScalar&amp;)</a>. </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#aafde38918912c9b562f44b0fc3b22589">&#9670;&nbsp;</a></span>logAbsDeterminant()</h2>

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<dl class="section return"><dt>Returns</dt><dd>the natural log of the absolute value of the determinant of the matrix of which *this is the QR decomposition. It has only linear complexity (that is, O(n) where n is the dimension of the square matrix) as the QR decomposition has already been computed.</dd></dl>
<dl class="section note"><dt>Note</dt><dd>This is only for square matrices.</dd>
<dd>
This method is useful to work around the risk of overflow/underflow that's inherent to determinant computation.</dd></dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="classEigen_1_1FullPivHouseholderQR.html#a1029e1ccc70bb8669043c5775e7f3b75">absDeterminant()</a>, <a class="el" href="classEigen_1_1MatrixBase.html#a7ad8f77004bb956b603bb43fd2e3c061">MatrixBase::determinant()</a> </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#ad26dd2d3c002939771d2375e4e051c28">&#9670;&nbsp;</a></span>matrixQ()</h2>

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<dl class="section return"><dt>Returns</dt><dd>Expression object representing the matrix Q </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#ab082b221dc32cf25a951f0f822b78337">&#9670;&nbsp;</a></span>matrixQR()</h2>

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<dl class="section return"><dt>Returns</dt><dd>a reference to the matrix where the Householder QR decomposition is stored </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#ac00d0f43ded3debd5c1769fd0a09c884">&#9670;&nbsp;</a></span>maxPivot()</h2>

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<dl class="section return"><dt>Returns</dt><dd>the absolute value of the biggest pivot, i.e. the biggest diagonal coefficient of U. </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a15bac4e5678baeb4f26c9b2fb588415d">&#9670;&nbsp;</a></span>nonzeroPivots()</h2>

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<dl class="section return"><dt>Returns</dt><dd>the number of nonzero pivots in the QR decomposition. Here nonzero is meant in the exact sense, not in a fuzzy sense. So that notion isn't really intrinsically interesting, but it is still useful when implementing algorithms.</dd></dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="classEigen_1_1FullPivHouseholderQR.html#a8f700c9adb9928a7cf801880946d66ff">rank()</a> </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a8f700c9adb9928a7cf801880946d66ff">&#9670;&nbsp;</a></span>rank()</h2>

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<dl class="section return"><dt>Returns</dt><dd>the rank of the matrix of which *this is the QR decomposition.</dd></dl>
<dl class="section note"><dt>Note</dt><dd>This method has to determine which pivots should be considered nonzero. For that, it uses the threshold value that you can control by calling <a class="el" href="classEigen_1_1FullPivHouseholderQR.html#ac86022d45b8b0ed0c004852affcb9ec6">setThreshold(const RealScalar&amp;)</a>. </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#ad136fe1c4b1ebd37aeb0e28c31386ffc">&#9670;&nbsp;</a></span>rowsTranspositions()</h2>

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<dl class="section return"><dt>Returns</dt><dd>a const reference to the vector of indices representing the rows transpositions </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#ac86022d45b8b0ed0c004852affcb9ec6">&#9670;&nbsp;</a></span>setThreshold() <span class="overload">[1/2]</span></h2>

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<p>Allows to prescribe a threshold to be used by certain methods, such as <a class="el" href="classEigen_1_1FullPivHouseholderQR.html#a8f700c9adb9928a7cf801880946d66ff">rank()</a>, who need to determine when pivots are to be considered nonzero. This is not used for the QR decomposition itself.</p>
<p>When it needs to get the threshold value, <a class="el" href="namespaceEigen.html" title="Namespace containing all symbols from the Eigen library.">Eigen</a> calls <a class="el" href="classEigen_1_1FullPivHouseholderQR.html#adbb357dc50ae6fa6f51eb785e9d85403">threshold()</a>. By default, this uses a formula to automatically determine a reasonable threshold. Once you have called the present method <a class="el" href="classEigen_1_1FullPivHouseholderQR.html#ac86022d45b8b0ed0c004852affcb9ec6">setThreshold(const RealScalar&amp;)</a>, your value is used instead.</p>
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<p>A pivot will be considered nonzero if its absolute value is strictly greater than \( \vert pivot \vert \leqslant threshold \times \vert maxpivot \vert \) where maxpivot is the biggest pivot.</p>
<p>If you want to come back to the default behavior, call <a class="el" href="classEigen_1_1FullPivHouseholderQR.html#ac20e4ce2bb07cd2f77fca60ad7a788f3">setThreshold(Default_t)</a> </p>

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<h2 class="memtitle"><span class="permalink"><a href="#ac20e4ce2bb07cd2f77fca60ad7a788f3">&#9670;&nbsp;</a></span>setThreshold() <span class="overload">[2/2]</span></h2>

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<p>Allows to come back to the default behavior, letting <a class="el" href="namespaceEigen.html" title="Namespace containing all symbols from the Eigen library.">Eigen</a> use its default formula for determining the threshold.</p>
<p>You should pass the special object Eigen::Default as parameter here. </p><div class="fragment"><div class="line">qr.setThreshold(Eigen::Default); </div>
</div><!-- fragment --><p>See the documentation of <a class="el" href="classEigen_1_1FullPivHouseholderQR.html#ac86022d45b8b0ed0c004852affcb9ec6">setThreshold(const RealScalar&amp;)</a>. </p>

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<h2 class="memtitle"><span class="permalink"><a href="#aad55fd4eaf0905b7dc092e7f1615b489">&#9670;&nbsp;</a></span>solve()</h2>

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<p>This method finds a solution x to the equation Ax=b, where A is the matrix of which <code>*this</code> is the QR decomposition.</p>
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<dl class="section return"><dt>Returns</dt><dd>the exact or least-square solution if the rank is greater or equal to the number of columns of A, and an arbitrary solution otherwise.</dd></dl>
<p>This method just tries to find as good a solution as possible. If you want to check whether a solution exists or if it is accurate, just call this function to get a result and then compute the error of this result, or use <a class="el" href="classEigen_1_1DenseBase.html#ae8443357b808cd393be1b51974213f9c">MatrixBase::isApprox()</a> directly, for instance like this:</p><div class="fragment"><div class="line"><span class="keywordtype">bool</span> a_solution_exists = (A*result).isApprox(b, precision); </div>
</div><!-- fragment --><p> This method avoids dividing by zero, so that the non-existence of a solution doesn't by itself mean that you'll get <code>inf</code> or <code>nan</code> values.</p>
<p>If there exists more than one solution, this method will arbitrarily choose one.</p>
<p>Example: </p><div class="fragment"><div class="line"><a class="code" href="group__matrixtypedefs.html#ga276bae130c142e906ad8f47d24d11c1c">Matrix3f</a> m = <a class="code" href="classEigen_1_1DenseBase.html#ae814abb451b48ed872819192dc188c19">Matrix3f::Random</a>();</div>
<div class="line"><a class="code" href="group__matrixtypedefs.html#ga276bae130c142e906ad8f47d24d11c1c">Matrix3f</a> y = <a class="code" href="classEigen_1_1DenseBase.html#ae814abb451b48ed872819192dc188c19">Matrix3f::Random</a>();</div>
<div class="line">cout &lt;&lt; <span class="stringliteral">&quot;Here is the matrix m:&quot;</span> &lt;&lt; endl &lt;&lt; m &lt;&lt; endl;</div>
<div class="line">cout &lt;&lt; <span class="stringliteral">&quot;Here is the matrix y:&quot;</span> &lt;&lt; endl &lt;&lt; y &lt;&lt; endl;</div>
<div class="line"><a class="code" href="group__matrixtypedefs.html#ga276bae130c142e906ad8f47d24d11c1c">Matrix3f</a> x;</div>
<div class="line">x = m.fullPivHouseholderQr().solve(y);</div>
<div class="line">assert(y.isApprox(m*x));</div>
<div class="line">cout &lt;&lt; <span class="stringliteral">&quot;Here is a solution x to the equation mx=y:&quot;</span> &lt;&lt; endl &lt;&lt; x &lt;&lt; endl;</div>
<div class="ttc" id="aclassEigen_1_1DenseBase_html_ae814abb451b48ed872819192dc188c19"><div class="ttname"><a href="classEigen_1_1DenseBase.html#ae814abb451b48ed872819192dc188c19">Eigen::DenseBase::Random</a></div><div class="ttdeci">static const RandomReturnType Random()</div><div class="ttdef"><b>Definition:</b> Random.h:114</div></div>
<div class="ttc" id="agroup__matrixtypedefs_html_ga276bae130c142e906ad8f47d24d11c1c"><div class="ttname"><a href="group__matrixtypedefs.html#ga276bae130c142e906ad8f47d24d11c1c">Eigen::Matrix3f</a></div><div class="ttdeci">Matrix&lt; float, 3, 3 &gt; Matrix3f</div><div class="ttdoc">3×3 matrix of type float.</div><div class="ttdef"><b>Definition:</b> Matrix.h:500</div></div>
</div><!-- fragment --><p> Output: </p><pre class="fragment">Here is the matrix m:
  0.68  0.597  -0.33
-0.211  0.823  0.536
 0.566 -0.605 -0.444
Here is the matrix y:
  0.108   -0.27   0.832
-0.0452  0.0268   0.271
  0.258   0.904   0.435
Here is a solution x to the equation mx=y:
 0.609   2.68   1.67
-0.231  -1.57 0.0713
  0.51   3.51   1.05
</pre> 
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<h2 class="memtitle"><span class="permalink"><a href="#adbb357dc50ae6fa6f51eb785e9d85403">&#9670;&nbsp;</a></span>threshold()</h2>

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template&lt;typename MatrixType_ &gt; </div>
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          <td class="memname">RealScalar <a class="el" href="classEigen_1_1FullPivHouseholderQR.html">Eigen::FullPivHouseholderQR</a>&lt; MatrixType_ &gt;::threshold </td>
          <td>(</td>
          <td class="paramname"></td><td>)</td>
          <td> const</td>
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<p>Returns the threshold that will be used by certain methods such as <a class="el" href="classEigen_1_1FullPivHouseholderQR.html#a8f700c9adb9928a7cf801880946d66ff">rank()</a>.</p>
<p>See the documentation of <a class="el" href="classEigen_1_1FullPivHouseholderQR.html#ac86022d45b8b0ed0c004852affcb9ec6">setThreshold(const RealScalar&amp;)</a>. </p>

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<hr/>The documentation for this class was generated from the following file:<ul>
<li><a class="el" href="FullPivHouseholderQR_8h_source.html">FullPivHouseholderQR.h</a></li>
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